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A C0-conforming DG finite element method for biharmonic equations on triangle/tetrahedron

  • Xiu Ye and Shangyou Zhang EMAIL logo


A C0-conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of C0 finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomials. This method, by its name, uses nonconforming (non C1) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete H2-norm and the L2-norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.

MSC 2010: 65N15; 65N30

Funding statement: Xiu Ye was supported in part by National Science Foundation Grant DMS-1620016.


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Received: 2021-02-16
Revised: 2021-12-15
Accepted: 2021-12-25
Published Online: 2022-09-14
Published in Print: 2021-12-30

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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